Corporate finance 7e ross ch17

17.1 Adjusted Present Value Approach17.2 Flows to Equity Approach 17.3 Weighted Average Cost of Capital Method 17.4 A Comparison of the APV, FTE, and WACC Approaches 17.5 Capital Budgeti

17

Capital Budgeting for

the Levered Firm

Recall that there are three questions in corporate

finance.

The first regards what long-term investments the firm

should make (the capital budgeting question).

The second regards the use of debt (the capital structure question).

This chapter considers the nexus of these questions.

Recall that there are three questions in corporate

finance.

The first regards what long-term investments the firm

should make (the capital budgeting question).

The second regards the use of debt (the capital structure question).

This chapter considers the nexus of these questions.

17.1 Adjusted Present Value Approach

17.2 Flows to Equity Approach

17.3 Weighted Average Cost of Capital Method

17.4 A Comparison of the APV, FTE, and WACC Approaches

17.5 Capital Budgeting When the Discount Rate Must Be Estimated 17.6 APV Example

17.7 Beta and Leverage

17.8 Summary and Conclusions

17.1 Adjusted Present Value Approach

17.2 Flows to Equity Approach

17.3 Weighted Average Cost of Capital Method

17.4 A Comparison of the APV, FTE, and WACC Approaches

17.5 Capital Budgeting When the Discount Rate Must Be Estimated 17.6 APV Example

17.7 Beta and Leverage

17.8 Summary and Conclusions

APV = NPV + NPVF

The value of a project to the firm can be thought

of as the value of the project to an unlevered firm

(NPV) plus the present value of the financing side effects (NPVF):

There are four side effects of financing :

The Tax Subsidy to Debt The Costs of Issuing New Securities The Costs of Financial Distress

Subsidies to Debt Financing

APV = NPV + NPVF

The value of a project to the firm can be thought

of as the value of the project to an unlevered firm

(NPV) plus the present value of the financing side effects (NPVF):

There are four side effects of financing :

The Tax Subsidy to Debt The Costs of Issuing New Securities The Costs of Financial Distress

Subsidies to Debt Financing

0 1 2 3 4

–$1,000 $125 $250 $375 $500

50 56

$

) 10 1 (

500

$ )

10 1 (

375

$ )

10 1 (

250

$ )

10 1 (

125

$ 000

, 1

$

% 10

4 3

2

% 10

The unlevered cost of equity is r 0 = 10%:

The project would be rejected by an all-equity firm: NPV < 0.

Consider a project of the Pearson Company, the timing and size of the incremental after-tax cash flows for an all-equity firm are:

The project would be

10

CF4 CF3

Now, imagine that the firm finances the project with

$600 of debt at r B = 8%

Pearson’s tax rate is 40%, so they have an interest tax

shield worth T C Br B = 40×$600×.08 = $19.20 each year.

Now, imagine that the firm finances the project with

$600 of debt at r B = 8%

Pearson’s tax rate is 40%, so they have an interest tax

shield worth T C Br B = 40×$600×.08 = $19.20 each year.

The net present value of the project under leverage is:

APV = NPV + NPV debt tax shield

$ 50

56

$

APV

09 7

$ 59

63 50

56

Note that there are two ways to calculate the NPV of the loan Previously, we calculated the PV of the interest tax shields Now, let’s calculate the actual NPV of the loan:

Note that there are two ways to calculate the NPV of the loan Previously, we calculated the PV of the interest tax shields Now, let’s calculate the actual NPV of the loan:

09 7

$ 59

63 50

56

$

) 08 1 (

600

$ )

08 1 (

) 4 1 ( 08 600

$ 600

APV = NPV + NPVF

NPV of the loan:

NPV of the loan:

CF2 CF1

F2 F1

CF0

3 –$28.80 =

8

PV of the interest tax shields.

CF1 F1

8

$19.20 = 40×$600×.08

$600×.08×(1–.40)

17.2 Flows to Equity Approach

Discount the cash flow from the project to the

equity holders of the levered firm at the cost of

levered equity capital, r S

There are three steps in the FTE Approach:

Step One: Calculate the levered cash flows

Step Two: Calculate r S

Step Three: Valuation of the levered cash flows at r S

Discount the cash flow from the project to the

equity holders of the levered firm at the cost of

levered equity capital, r S

There are three steps in the FTE Approach:

Step One: Calculate the levered cash flows

Step Two: Calculate r S

Step Three: Valuation of the levered cash flows at r S

Since the firm is using $600 of debt, the equity holders only have

to come up with $400 of the initial $1,000.

Thus, CF 0 = –$400

Each period, the equity holders must pay interest expense The

after-tax cost of the interest is B×r B ×(1 – T C ) = $600×.08×(1 – 40)

= $28.80

Since the firm is using $600 of debt, the equity holders only have

to come up with $400 of the initial $1,000.

Thus, CF 0 = –$400

Each period, the equity holders must pay interest expense The

after-tax cost of the interest is B×r B ×(1 – T C ) = $600×.08×(1 – 40)

) )(

4 3

20

19 )

10 1 (

500

$ )

10 1 (

375

$ )

10 1 (

250

$ )

10 1 (

08 10 )(.

40 1

( 09 407

$

600

$ 10

B V

To calculate the debt to equity ratio, , start with

Step Three: Valuation for Pearson

Discount the cash flows to equity holders at r S = 11.77%

Discount the cash flows to equity holders at r S = 11.77%

56 28

$

) 1177

1 (

80 128

$ )

1177

1 (

20 346

$ )

1177

1 (

20 221

$ )

1177

1 (

20 96

$ 400

Step Three: Valuation for Pearson

CF2 CF1

17.3 WACC Method for Pearson

To find the value of the project, discount the unlevered cash flows at the weighted average cost of capital.

Suppose Pearson’s target debt to equity ratio is 1.50

To find the value of the project, discount the unlevered cash flows at the weighted average cost of capital.

Suppose Pearson’s target debt to equity ratio is 1.50

) 1

B S

B S

B r

B S

) 40 1 (

%) 8 ( ) 60 0 (

%) 77 11 ( ) 40 0

S

B

 50

60

0 5

2

5

1 5

1

5

S

S S

Valuation for Pearson using WACC

To find the value of the project, discount the

unlevered cash flows at the weighted average cost

of capital

To find the value of the project, discount the

unlevered cash flows at the weighted average cost

of capital

4 3

500

$ )

0758

1 (

375

$ )

0758

1 (

250

$ )

0758

1 (

125

$ 000

, 1

Valuation for Pearson using WACC

CF2 CF1

and WACC Approaches

All three approaches attempt the same

task:valuation in the presence of debt financing.

Guidelines:

Use WACC or FTE if the firm’s target debt-to-value

ratio applies to the project over the life of the project.

Use the APV if the project’s level of debt is known

over the life of the project.

In the real world, the WACC is the most widely

used by far.

All three approaches attempt the same

task:valuation in the presence of debt financing.

Guidelines:

Use WACC or FTE if the firm’s target debt-to-value

ratio applies to the project over the life of the project.

Use the APV if the project’s level of debt is known

over the life of the project.

In the real world, the WACC is the most widely

used by far.

Summary: APV, FTE, and WACC

Initial Investment All All Equity Portion

Discount Rates r 0 r WACC r S

PV of financing effects Yes No No

Which approach is best?

Use APV when the level of debt is constant

Use WACC and FTE when the debt ratio is constant

WACC is by far the most common FTE is a reasonable choice for a highly levered firm

Initial Investment All All Equity Portion

Discount Rates r 0 r WACC r S

PV of financing effects Yes No No

Which approach is best?

Use APV when the level of debt is constant

Use WACC and FTE when the debt ratio is constant

WACC is by far the most common FTE is a reasonable choice for a highly levered firm

Discount Rate Must Be Estimated

A scale-enhancing project is one where the project is

similar to those of the existing firm.

In the real world, executives would make the

assumption that the business risk of the

non-scale-enhancing project would be about equal to the business risk of firms already in the business.

No exact formula exists for this Some executives might select a discount rate slightly higher on the assumption that the new project is somewhat riskier since it is a new entrant.

A scale-enhancing project is one where the project is

similar to those of the existing firm.

In the real world, executives would make the

assumption that the business risk of the

non-scale-enhancing project would be about equal to the business risk of firms already in the business.

No exact formula exists for this Some executives might select a discount rate slightly higher on the assumption that the new project is somewhat riskier since it is a new entrant.

17.6 APV Example:

Worldwide Trousers, Inc is considering replacing a $5

million piece of equipment The initial expense will be depreciated straight-line to zero salvage value over 5 years; the pretax salvage value in year 5 will be

$500,000 The project will generate pretax savings of

$1,500,000 per year, and not change the risk level of the firm The firm can obtain a 5-year $3,000,000 loan

at 12.5% to partially finance the project If the project were financed with all equity, the cost of capital would

be 18% The corporate tax rate is 34%, and the risk-free rate is 4% The project will require a $100,000

investment in net working capital.  Calculate the APV.

Worldwide Trousers, Inc is considering replacing a $5

million piece of equipment The initial expense will be depreciated straight-line to zero salvage value over 5 years; the pretax salvage value in year 5 will be

$500,000 The project will generate pretax savings of

$1,500,000 per year, and not change the risk level of the firm The firm can obtain a 5-year $3,000,000 loan

at 12.5% to partially finance the project If the project were financed with all equity, the cost of capital would

be 18% The corporate tax rate is 34%, and the risk-free rate is 4% The project will require a $100,000

investment in net working capital.  Calculate the APV.

17.6 APV Example: Cost

25 561 ,

873 ,

4

$

) 1

(

) 34 1 ( 000 ,

500 )

1 (

000 ,

100 1

5

0 5

m

Cost

f

The cost of the project is not $5,000,000.

We must include the round trip in and out of net working capital and the after-tax salvage value

Let’s work our way through the four terms in this equation:

NWC is riskless, so we discount it at r f Salvage value should

have the same risk as the rest of the firm’s assets, so we use r 0

17.6 APV Example: PV unlevered project

is the present value of the unlevered cash flows discounted at the unlevered cost of capital, 18%.

Turning our attention to the second term,

899 ,

095 ,

3

$

) 18 1 (

) 34 1 ( 5

1

$ )

1 (

5 1

t

project unlevered

PV

m r

UCF PV

depreciation tax shield

is the is the present value of the tax savings due to

depreciation discounted at the risk free rate: r f = 4%

Turning our attention to the third term,

619 ,

513 ,

1

$ )

04 1 (

34 1

$

) 1

(

5 1

5 1

T D

17.6 APV Example: PV interest tax shield

is the present value of the tax savings due to interest

expense discounted at the firm’s debt rate: r D = 12.5%

Turning our attention to the last term,

46 972 ,

453 )

125

1 (

500 ,

127

) 125

1 (

3

$ 125

0 34

0 )

1 (

3

$

5

1 shield

tax interest

5 1

5

1 shield

tax interest

PV

m r

m r

T PV

Since the project has a positive APV, it looks like a go.

Let’s add the four terms in this equation:

17.7 Beta and Leverage

Recall that an asset beta would be of the form:

2 Market

Asset

σ

) ,

(

17.7 Beta and Leverage: No Corp.Taxes

In a world without corporate taxes, and with riskless corporate

debt, ( Debt = 0 ) it can be shown that the relationship between the beta of the unlevered firm and the beta of levered equity is:

In a world without corporate taxes, and with riskless corporate

debt, ( Debt = 0 ) it can be shown that the relationship between the beta of the unlevered firm and the beta of levered equity is:

In a world without corporate taxes, and with risky corporate

debt, it can be shown that the relationship between the beta of the unlevered firm and the beta of levered equity is:

EquityDebt

Asset

Equity β

Asset Debt

17.7 Beta and Leverage: with Corp Taxes

In a world with corporate taxes, and riskless debt,

it can be shown that the relationship between the beta of the unlevered firm and the beta of levered equity is:

In a world with corporate taxes, and riskless debt,

it can be shown that the relationship between the beta of the unlevered firm and the beta of levered equity is:

firmUnlevered

Equity

Debt 1

levered firm, it follows that  Equity >  Unlevered firm

with Corp Taxes

If the beta of the debt is non-zero, then:

17.8 Summary and Conclusions

1 The APV formula can be written as:

2 The FTE formula can be written as:

3 The WACC formula can be written as

1 The APV formula can be written as:

2 The FTE formula can be written as:

3 The WACC formula can be written as

investment

Initial debt

of effects

Additional )

1 (

Initial )

1 (

investment

Initial )

1 (

r UCF NPV

17.8 Summary and Conclusions

4 Use the WACC or FTE if the firm's target debt to

value ratio applies to the project over its life.

 WACC is the most commonly used by far.

 FTE has appeal for a firm deeply in debt.

5 The APV method is used if the level of debt is

known over the project’s life.

 The APV method is frequently used for special

situations like interest subsidies, LBOs, and leases.

6 The beta of the equity of the firm is positively

related to the leverage of the firm.

4 Use the WACC or FTE if the firm's target debt to

value ratio applies to the project over its life.

 WACC is the most commonly used by far.

 FTE has appeal for a firm deeply in debt.

5 The APV method is used if the level of debt is

known over the project’s life.

 The APV method is frequently used for special

situations like interest subsidies, LBOs, and leases.

6 The beta of the equity of the firm is positively

related to the leverage of the firm.

Example: Hamilos Worldwide

Hamilos Worldwide is considering a $5 million expansion of their existing business The initial expense will be

depreciated straight-line over 5 years to zero salvage value; the pretax salvage value in year 5 will be $500,000 The

project will generate pretax gross earnings of $1,500,000 per year, and not change the risk level of the firm Hamilos can obtain a 5-year 12.5% loan to partially finance the project Flotation costs are 1% of the proceeds If undertaken, this project should maintain a target D/E ratio of 1.50 If the project were financed with all equity, the cost of capital would be 18% The corporate tax rate is 30%, and the risk- free rate is 6% The project will require a $100,000

investment in net working capital.

Hamilos Worldwide is considering a $5 million expansion of their existing business The initial expense will be

depreciated straight-line over 5 years to zero salvage value; the pretax salvage value in year 5 will be $500,000 The

project will generate pretax gross earnings of $1,500,000 per year, and not change the risk level of the firm Hamilos can obtain a 5-year 12.5% loan to partially finance the project Flotation costs are 1% of the proceeds If undertaken, this

project should maintain a target D/E ratio of 1.50 If the

project were financed with all equity, the cost of capital

would be 18% The corporate tax rate is 30%, and the free rate is 6% The project will require a $100,000

risk-investment in net working capital.